Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group

We show that a class of integral operators on the Heisenberg group, given by the off-diagonal decay of the kernel, is inverse-closed. Using this result, we obtain a version of Wiener's lemma for convolution on the Heisenberg group. The same approach yields a similar result for a class of pseudodifferential operators.

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